linear-quadratic-Gaussian control

These problems are dual and together they solve the linear-quadratic-Gaussian control problem (LQG).

Another example is the separation of the linear-quadratic-Gaussian control solution into the Kalman filter and optimal controller for a linear-quadratic regulator.

Linear-quadratic-Gaussian control (LQG)

Rudy Kalman (Kalman filter) later reformulated this in terms of state-space smoothing and prediction where it is known as the linear-quadratic-Gaussian control problem.

It is a counterexample to a natural conjecture that one can generalize a key result of centralized linear-quadratic-Gaussian control systems: that affine (linear) control laws are optimal.

These are Model Predictive Control (MPC) and linear-quadratic-Gaussian control (LQG).

More generally, the term "Riccati equation" is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control.

Together with the linear-quadratic regulator (LQR), the Kalman filter solves the linear-quadratic-Gaussian control problem (LQG).

Assuming a quadratic form for the value function, we obtain the usual Riccati equation for the Hessian of the value function as is usual for Linear-quadratic-Gaussian control.

In general, if the separation principle applies, then filtering also arises as part of the solution of an optimal control problem, i.e. the Kalman filter is the estimation part of the optimal control solution to the Linear-quadratic-Gaussian control problem.